Step 1: Understanding contraction effect.
Both lanthanoid and actinoid series show contraction due to poor shielding effect of $f$-electrons, leading to a gradual decrease in atomic and ionic radii.
Step 2: Comparison of shielding.
In actinoids, the $5f$-electrons have even poorer shielding compared to $4f$-electrons of lanthanoids. Additionally, relativistic effects are more prominent in actinoids.
Step 3: Analysis of given statements.
Lanthanoids form fewer complexes than actinoids, actinoid hydroxides are generally more basic, and $4f$-orbitals are more deeply buried (higher binding energy) than $5f$-orbitals.
Step 4: Conclusion.
Hence, the correct statement is (B) Actinoid contraction is greater than lanthanoid contraction.